Question

In the given figure two parallel lines l,m are intersected by a tranversal. If $\angle 1={105}^{\circ }$ then $\angle 7$ and $\angle 8$ are

• A. ${45}^{\circ },{135}^{\circ }$
• B. ${105}^{\circ },{75}^{\circ }$
• C. ${75}^{\circ },{105}^{\circ }$
• D. ${95}^{\circ },{85}^{\circ }$

Answer 1

The correct option is B

${105}^{\circ },{75}^{\circ }$

Given,$l\parallel m$ and $\angle 1={105}^{\circ }$

$\angle 1=\angle 7$ [ Exterior alternate angles]

$\angle 7={105}^{\circ }$

$\angle 7+\angle 8={180}^{\circ }$ [ Linear Pair]

$\Rightarrow {105}^{\circ }+\angle 8={180}^{\circ }$

$\Rightarrow \angle 8={180}^{\circ }-{105}^{\circ }={75}^{\circ }$